16 June 2014
We investigate the dynamics of a class of tumor growth models known as mixed models. The key characteristic of these type of tumor growth models is that the different populations of cells are continuously present everywhere in the tumor at all times. In this work we focus on the evolution of tumor growth in the presence of proliferating, quiescent and dead cells as well as a nutrient. The system is given by a multi-phase flow model and the tumor is described as a growing continuum such that both the domain occupied by the tumor as well as its boundary evolve in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion and viscosity in the weak formulation. Further extensions will be discussed. This is joint work with D. Donatelli.
- Partial Differential Equations Seminar